Can I use my old imac's monitor with a new mini mac?

A product called ScreenRecycler can be used for this purpose, but a standalone monitor is needed for the initial setup.

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To output to a TV, if it doesn't have a VGA or DVI input, you'll need a DVI/S-video adaptor. With one of those, then yes you could use the TV as a display to get the mini set up, as long as your TV has s-video or composite input.

From the ScreenRecycler page Neil gave:
"Many Mac users have a second computer sitting right next to their main computer on their desk including a nice display. ScreenRecycler now enables you to use this spare computer as second display for your Mac. You can even use an idle machine for that purpose.
It’s like a dual monitor setup without the need to buy an additional monitor.
Just start ScreenRecycler on your Mac then connect to ScreenRecycler via VNC from your second machine.

Use any machine as additional monitor on your Mac !"

Meaning that no, the iMac won't just be a monitor for the mini - it can't work that way because there's no way to get the mini's video out into the iMac. What happens is that you network to two systems together and use software such as VNC (a remote access application) on the iMac to access the mini, and ScreenRecycler will then show the mini's video output on the imac screen.

More complex than a simple matter of connecting a display, and not entirely satisfactory, but workable.

+so what type of Cable would I then connect the mac Mini to my old iMac?+

You just use a standard ethernet cable (looks like a slightly bigger version of a modular phone cord.)

(Some people may suggest a variant version, the "cross-over" ethernet cable, but AFAIK the new Minis take care of the cross-over automatically for you, so you can use a standard ethernet cable.)

Or you can just connect both devices to a router (or airport).

I will repeat what has already been said, that running a Mini this way will detract somewhat from the Mac experience.